Quantum tomography of helicity states for general scattering processes
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929525070233600 |
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| author | Bernal, Alexander |
| author_facet | Bernal, Alexander |
| contents | Quantum tomography has become an indispensable tool in order to compute the density matrix $ρ$ of quantum systems in Physics. Recently, it has further gained importance as a basic step to test entanglement and violation of Bell inequalities in High-Energy Particle Physics. In this work, we present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process. In particular, we perform an expansion of $ρ$ over the irreducible tensor operators $\{T^L_M\}$ and compute the corresponding coefficients uniquely by averaging, under properly chosen Wigner D-matrices weights, the angular distribution data of the final particles. Besides, we provide the explicit angular dependence of both the normalised differential cross section and the generalised production matrix $Γ$. Finally, we re-derive all our previous results from a quantum-information perspective using the Weyl-Wigner-Moyal formalism and we obtain in addition simple analytical expressions for the Wigner $P$ and $Q$ symbols. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10838 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum tomography of helicity states for general scattering processes Bernal, Alexander High Energy Physics - Phenomenology High Energy Physics - Theory Quantum Physics Quantum tomography has become an indispensable tool in order to compute the density matrix $ρ$ of quantum systems in Physics. Recently, it has further gained importance as a basic step to test entanglement and violation of Bell inequalities in High-Energy Particle Physics. In this work, we present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process. In particular, we perform an expansion of $ρ$ over the irreducible tensor operators $\{T^L_M\}$ and compute the corresponding coefficients uniquely by averaging, under properly chosen Wigner D-matrices weights, the angular distribution data of the final particles. Besides, we provide the explicit angular dependence of both the normalised differential cross section and the generalised production matrix $Γ$. Finally, we re-derive all our previous results from a quantum-information perspective using the Weyl-Wigner-Moyal formalism and we obtain in addition simple analytical expressions for the Wigner $P$ and $Q$ symbols. |
| title | Quantum tomography of helicity states for general scattering processes |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2310.10838 |